Bamboo flooring, can it be layed over old hardwood floors or would it be better to put a layer of plywood?

I currently have a damaged hardwood floor that is over 100 years old. I want to install prefinished bamboo floors over it. Some of the damaged spots have been replaced with plywood, but there are still some creaky spots. Should I install a think sheet of plywood over the hardwood and then the bamboo on top? Or is it ok just to put the bamboo over the hardwood? Also I was told to lay it vertical to the hardwood floor, is that best? Or should I lay it on a diagnal so that every plank is resting on a beam?

you should remove the old hard floor and then put bamboo